The average amount of money that a student at Stanford University carries on his/her person is $45 with a standard deviation of $10. What is the probability that a random sample of 12 Stanford...

The average amount of money that a student at Stanford University carries on his/her person is $45 with a standard deviation of $10. What is the probability that a random sample of 12 Stanford University students will have an average of less than $50 on them? (Give your answer as a decimal rounded to 4 decimal places)

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violy | High School Teacher | (Level 1) Associate Educator

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We will apply the formula for the z-score for sample mean.

`z = (barx - mu)/((sigma)/(sqrt(n)))`

Identifying the values given.

`mu = 45` , `sigma = 10` , `n = 12` , `barx = 50`

Plug-in the values on the formula.

`z = (barx - mu)/((sigma)/sqrt(n))`

`= (50 - 45)/((10/(sqrt(12))))`

`= 5/((10)/(3.464101615))`

`= 5/(2.886751346)`

`z = 1.73`

Since we are asked to find the probability that a random sample of 12 Standford University students will have an average of less than $50 on them, we will consider the area to the left of` z = 1.73` . Prefer on a z-table.

I attached a z-table which you can used. 

Therefore, the probability is 0.9582.

Method on finding the probability using a calculator:

Press 2nd then VARS, then press `2` for the normalcdf.

It is in the form normalcdf(lower, upper, mean, sd).

So, we will input normalcdf(-1000,1.73,0,1) , then press ENTER.

Therefore, the probability is 0.9582.

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